|Workshop on Representation Theory and Analysis on Locally Symmetric Spaces|
|Topic:||Ax-Schanuel for Shimura Varieties|
|Affiliation:||University of Toronto|
|Date:||Friday, March 9|
|Time/Room:||11:30am - 12:30pm/Simonyi Hall 101|
Abstract: (joint with N.Mok, J.Pila) Shimura varieties (S) are uniformized by symmetric spaces (H), and the uniformization map Pi:H --> S is quite transcendental. Understanding the interaction of this map with the two algebraic structures is of particular interest in arithmetic, as it is a necessary ingredient for the modern approaches to the Andre-Oort and Zilber-Pink conjectures, as well As a new approac to Shafarevich type theorems about integral points on varieties. We establish an analogue of the Ax-Schanuel theorem in this context, which essentially says that any atypical algebraic relations between subvarieties in H and S are governed by Shimura subvarieties.